∀P.Leo III

Leo III - A Massively Parallel Higher-Order Theorem Prover

2nd place for Leo-III in CASC-26 THF division
Leo-III 1.1 reached 2nd place in this year's CASC-26 in the THF division!
Check out the results at CASC results page!

Overview

The automated theorem proving systems LEO-I and LEO-II have found international acclaim as
very successful reasoners for classical higher-order logic. Novel contributions of LEO-I include
a native (versus axiomatic) treatment of the extensionality principles and the cooperation with
external reasoners (such as the first-order prover E) via a flexible agent architecture. The implementation
of LEO-II did significantly influence the parallel development of the new higher-order
TPTP THF infrastructure for typed higher-order logics, which in turn has led to major system
improvements (e.g. in the automated theorem provers ISABELLE/HOL and TPS) and to new
systems developments (such as Satallax) for classical higher-order logic. LEO-II has won the international
CASC competitions in 2010 and it has been integrated in the interactive proof
assistant ISABELLE /HOL.

In this project, we want to turn LEO-II into a state-of-the-art theorem prover based on ordered paramodulation/
superposition.
In constrast to LEO-II, we replace the internal term representation
(the commonly used simply typed lambda calculus) by a more expressive system
supporting type polymorphism. In the course of the project, we plan to further
enhance the type system with type classes and type constructors similar to System Fω .
In order to achieve a substantial performance speed-up,
the architecture of Leo-III will be based on massive parallelism
(e.g. And/Or-Parallelism, Multisearch).

The current design is a multi-agent blackboard architecture
that will allow to independently run agents with our proof calculus as well as
agents for external (specialized) provers.
Leo-III will focus right from the start on compatibility
to the widely used TPTP infrastructure. Moreover,
it will offer built-in support for specialized external
prover agents and provide external interfaces to interactive
provers such as Isabelle/HOL.
The implementation
will excessively use term sharing and
several indexing techniques. Leo-III will
also offer special support for reasoning in various quantified non-classical
logics by exploiting a semantic embedding approach.

The Leo-III project is supported by the German National Research Foundation (DFG) under grant BE 2501/11-1 (LEO-III).

LEOPARD
(Leo-III's Parallel ARchitecture and Datastructures)
is a generic system platform for implementing knowledge representation and reasoning tools
(such as automated theorem prover) based on classical higher-order logic.
The first relase of LeoPARD can be found
at its
GitHub repository.

Alexander Steen and Max Wisniewski,
Embedding of First-Order Nominal Logic into HOL.
5th World Congress and School on Universal Logic, Istanbul, 2015.

Christoph BenzmÜller and Bruno Woltzenlogel Paleo,
On Logic Embeddings and Gödel’s God.
In Proceedings of the 22nd International Workshop on Algebraic Development Techniques (WADT 2014),
Sinaia, Romania, 2014.